Post on 29-Apr-2023
Catena 61 (2005) 210–228
www.elsevier.com/locate/catena
Evaluating the MEFIDIS model for runoff and soil
erosion prediction during rainfall events
Joao Pedro Nunes*, Goncalo Nuno Vieira, Julia Seixas,
Pedro Goncalves, Nuno Carvalhais
Environmental Systems Analysis Group (GASA), Department of Environmental Sciences and Engineering,
Faculty of Sciences and Technology, New University of Lisbon, GASA-DCEA/FCT,
Quinta da Torre, 2829-516 Caparica, Portugal
Abstract
MEFIDIS–short for Physically Based Distributed Erosion Model–was developed to simulate the
consequences of climate and land-use changes for surface runoff and erosion patterns during extreme
rainfall events. The model relies on physically based runoff and soil detachment equations, dividing
the simulation area into spatial homogeneous units and using a dynamic approach for runoff and
suspended sediment distribution. It was evaluated with measured runoff and net erosion data for 16
events in the Lucky Hills 103 (USA) and Ganspoel (Belgium) catchments, using a single parameter
set for each catchment and simple assumptions (wet or dry) on pre-storm soil moisture. The model
was applied with a resolution of 5�5 m and 1-s time-steps. Observed soil erosion patterns in
Ganspoel were also used in the evaluation exercise.
Overall, simulation results have a good correlation with measured data (ranging from 0.85 to
0.96). Model precision was less satisfactory (average unsigned error ranging from 37% to 47%),
but it still fell well below the variability of the events (two orders of magnitude for runoff and
net erosion). Part of the simulation errors appear to be linked with variability in runoff and
erosion measurements. The calibrated model for Ganspoel required two parameter sets for
crusted and non-crusted conditions for half of the analyzed land-use classes; better calibration of
parameters associated with crusting significantly improved model performance for this
catchment. Despite this problem, MEFIDIS was shown to perform well for the range of
selected events.
0341-8162/$ -
doi:10.1016/j.c
* Correspond
E-mail add
see front matter D 2005 Elsevier B.V. All rights reserved.
atena.2005.03.005
ing author. Tel./fax: +351 212948374.
ress: jpcn@fact.unl.pt (J.P. Nunes).
J.P. Nunes et al. / Catena 61 (2005) 210–228 211
Within-watershed simulated runoff in Lucky Hills 103 compared well with measured results.
In Ganspoel, the simulated erosion patterns did not compare well with observed patterns;
however, simulated erosion sources were located inside the fields where erosion features were
observed, and within a distance of 65 m. The model has therefore the potential to predict
sediment sources inside a catchment, but the high resolution results should be used only as an
indicator.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Modeling soil erosion; Spatially distributed modeling; Model calibration; Soil erosion patterns
1. Introduction
Recent research suggests that climatic instability will increase as a consequence of
global climate change, resulting in greater frequency and intensity of extreme weather
events (McCarthy et al., 2002; Milly et al., 2002; Senior et al., 2002). One potential
consequence will be the acceleration of soil erosion rates, responding to changes both in
rainfall volume and intensity, with consequences for topsoil degradation, loss of
agricultural productivity and increased export of sediment and contaminants from
agricultural fields (Toy et al., 2002; SWCS, 2003).
The prediction potential of soil loss rates has improved steadily, from the average
annual estimations using the Universal Soil Loss Equation approach (Wischmeier and
Smith, 1978) to increasingly complex soil erosion models capable of estimating the
consequences of single rainfall events (Favis-Mortlock et al., 2001; Morgan and
Quinton, 2001; Toy et al., 2002). Recent event-based models include EUROSEM
(Morgan et al., 1998), KINEROS (Smith et al., 1995), LISEM (de Roo et al., 1996a,b)
and WEPP (Flanagan and Nearing, 1995). Overall, and despite improved spatial and
temporal discretization and better process description, simulation results are highly
variable and very sensitive to input parameters (Wu et al., 1993; Jetten et al., 1999,
2003).
This uncertainty can be related with variability in model input data, and with the non-
linear nature of the runoff and erosion processes themselves (Morgan and Quinton, 2001;
Jetten et al., 2003). Although model results can generally be improved by calibration,
calibrating for future conditions is not possible; this calls into question the robustness of
runoff and erosion models for climate change analysis (Beven, 2000; Morgan and
Quinton, 2001). A robust model should be able to reasonably perform with similar
parameter values, including highly dynamic ones, for the widest possible range of
conditions (Toy et al., 2002).
This research article presents and evaluates the MEFIDIS (Modelo de Erosao FIsico e
DIStribuıdo—Spatially Distributed Physical Erosion Model) soil erosion model. MEFI-
DIS was developed to assess the risk posed by unusually intense storm events for flooding
and land degradation in medium-sized watersheds, in particular due to climate and land-
use changes. It combines a raster-based approach to spatial distribution, allowing a
detailed prediction of erosion patterns (Jetten et al., 2003), with a fully dynamic approach
to predict time-variable hydrographs. Although this increases the computational power
J.P. Nunes et al. / Catena 61 (2005) 210–228212
needed to run the model, it was not considered a significant problem for the purposes
stated above.
The robustness of MEFIDIS for climate and land-use change assessment was evaluated
using outlet measurements for a semi-arid natural catchment, Lucky Hills 103 (USA), and
a humid agricultural catchment, Ganspoel (Belgium). The model was run using a single
parameter set for each catchment and simple assumptions on soil moisture content (dry or
wet). The quality of within-watershed predictions was also evaluated using runoff
measurements at a point inside Lucky Hills 103 and observed erosion and deposition
patterns in Ganspoel.
2. Study areas
Lucky Hills 103 (Fig. 1, top) is a small (3.7 ha) instrumented catchment inside
the Walnut Gulch test watershed, Arizona. A small nested catchment, Lucky Hills
101 (1.3 ha), is also instrumented for runoff measurement. This area represents a
semi-arid rangeland with a gravelly sandy-loam soil, covered with rocks and shrub
vegetation.
The Ganspoel watershed (Fig. 1, bottom) is a larger catchment (111 ha), representative
of a temperate agricultural area over the European loess belt. Soils in this region are very
prone to crusting, a condition which leads to decreased permeability and increased runoff
and erosion (Cerdan et al., 2001). The catchment is subdivided into ca. 80 fields with crops
varying with season: typical crops are winter cereals followed by maize or a root crop,
such as beet or potatoes.
Four land-use cases were studied: May 1997, dominated by beet, winter cereals and
summer cereals; July 1997, with the same occupation as in May but with crops in a latter
stage of development; August 1998, dominated by beet, potatoes and winter cereals; and
September 1998, with the same occupation as in August except that winter cereals were
harvested.
3. Methods
3.1. The MEFIDIS model
MEFIDIS–the Portuguese acronym for Physically Based Distributed Erosion Model–
simulates erosion patterns inside watersheds caused by single rainfall events. The
modeling approach is deterministic, physically based, spatially distributed and dynamical
in time. It was applied to Ganspoel and Lucky Hills 103 with a spatial resolution of 5�5
m and 1-s time-steps.
Erosion simulation can be divided in two parallel phases: runoff generation and soil
detachment (Wu et al., 1993). Fig. 2 shows the processes taken into account by MEFIDIS,
following Chow et al. (1988) and Foster (1982). Both Hortonian and saturation excess
runoff generation processes are taken into account. Soil detachment is simulated for
interrill and rill areas as, respectively, rain splash and flow erosion. Runoff flow is
Fig. 1. The Lucky Hills 103 (top) and Ganspoel (bottom) catchments, with 5-m contour lines; darker lines
represent the Lucky Hills 101 nested catchment (top) and field boundaries in Ganspoel (bottom).
J.P. Nunes et al. / Catena 61 (2005) 210–228 213
computed as a kinematic wave (Chow et al., 1988); suspended sediment flow is calculated
using the transport capacity approach (Foster, 1982).
The approach to spatially distributed modeling is also shown in Fig. 2. The simulation
area is divided into an orthogonal matrix of square cells, assumed to represent
homogenous conditions; runoff generation and soil detachment are computed for each
cell. Resulting overland flow and suspended sediment are routed between cells following
the steepest slope. Temporal dynamics are handled by solving the model’s governing
equations in discrete, successive time-steps.
Fig. 2. Spatial discretization scheme in regular cells used by the model (left); the processes simulated by the
model within each cell and at the boundaries between cells are also shown (right).
J.P. Nunes et al. / Catena 61 (2005) 210–228214
3.1.1. Mathematical formulation
MEFIDIS uses the St. Venant equations to simulate runoff generation and routing
(Chow et al., 1988). The continuity equation takes into account interception and
infiltration, using the following form:
BQ
Bxþ BA
Bt¼ R� I � F ð1Þ
where Q is the surface flow rate (m3/s), A is the surface flow cross-sectional area (m2), R is
the rainfall rate (m/s), I is the interception storage rate (m/s), F is the infiltration rate (m/s),
and x and t are respectively the spatial (m) and temporal (s) dimensions.
Evapotranspiration and subsurface lateral flow are not simulated as in most cases they
occur on a time-scale greater than a single event (Chow et al., 1988). Eq. (1) is solved with
a finite difference approximation using a Forward-Time Backward-Space (FTBS) explicit
scheme (Huggins and Burney, 1982; Chapra, 1997). This method requires the use of very
short time-steps in order to insure the stability of the results.
The interception rate is calculated following Linsley et al. (1975) as a function of the
maximum interception storage capacity and the vegetation cover fraction. The infiltration
rate for each time-step is calculated using the Green–Ampt method (Chow et al., 1988):
F ¼ Ksat
w 1� Sið ÞhFc
þ 1
��ð2Þ
where F is the infiltration rate (mm/h), Ksat is the saturated hydraulic conductivity of the
soil (mm/h), w is the soil matric potential (mm), Si is the soil moisture saturation at the
start of the event, h is the soil porosity, and Fc is the cumulative infiltration (mm).
A fraction of surface runoff is held in depression storage, estimated from the maximum
surface storage capacity and the lateral inflow rate (R–I–F in Eq. (1)) following Linsley et
al. (1975). The outflow rate for the remaining surface runoff is calculated using a
kinematic wave approach (Chow et al., 1988):
Q ¼ A5=3S1=2
nP2=3ð3Þ
J.P. Nunes et al. / Catena 61 (2005) 210–228 215
where S is the surface slope (m/m), n is Manning’s roughness coefficient, P is the
perimeter of the surface flow (m), and Q and A are as defined for Eq. (1).
Flow width is calculated from the fraction of the cell covered by water, which is
approximated by the relationship between surface runoff height and the maximum
depression storage capacity. Since the model calculates the outflow rate for each cell,
inflow rates become the outflow rates from neighboring upstream cells, which results in a
one-dimensional approximation of two-dimensional flow (Chow et al., 1988).
Soil detachment and transport is handled with the continuity equation described by
Foster (1982) and Chapra (1997), taking into account interrill and rill sediment delivery
rates, inflow and outflow. Sedimentation occurs when the rill sediment delivery rate is
negative. The equation is:
B ACsedð ÞBt
þ B QCsedð ÞBx
¼ Ds þ Dr ð4Þ
where Csed is the sediment concentration in the flow (kg/m3), Ds and Dr are respectively
the interrill and rill sediment delivery rate (kg/s), and A, Q, t and x are as defined for
Eq. (1).
Gully erosion processes are not simulated due to the uncertainty associated with current
models (Nachtergaele et al., 2001; Jetten et al., 2003). Eq. (4) is solved with a finite
difference approximation, using a FTBS explicit scheme.
Sediment delivery from interrill zones is assumed to be entirely from rainfall splash
erosion (Foster, 1982; Toy et al., 2002). The splash detachment rate is calculated following
Sharma et al. (1991, 1993):
Ds ¼ KpE i� icð ÞRhRcAs ð5Þ
where Kp is the soil detachability by a single drop (kg/J), E is the effective kinetic energy
of rainfall (J/m3), i and ic are respectively the rainfall rate and a threshold rainfall rate for
soil detachment initiation (m/s), Rh is a dampening ratio due to surface water, Rc is the
fractional cover of vegetation and paved areas, As is the area of a model cell (m2) and Ds is
as described for Eq. (4).
Soil detachability, kinetic energy of rainfall and the critical rainfall rate are all a function
of the critical shear stress and the clay mass fraction of the soil. Dampening by surface water
is related with raindrop diameter following the work of Ferreira and Singer (1985).
Soil detachment and deposition in rills are simulated as a result of runoff flow,
following the sediment transport capacity approach: if suspended sediment is lower than
this capacity, detachment occurs, otherwise excess soil sediments (Foster, 1982; Govers,
1990). The equation is:
Dr ¼ Y Tc � Csedð Þusedwdx ð6Þ
where Y is the detachment/deposition efficiency factor, Tc is the sediment transport
capacity of the surface flow (kg/m3), Csed is the sediment concentration in the surface flow
(kg/m3), used is the particle sedimentation velocity (m/s), w and dx are respectively the
flow width and length (m), and Dr is as defined for Eq. (4).
Detachment rate efficiency is calculated from a relationship with the soil critical shear
stress; complete efficiency is considered in the case of sediment deposition (Rauws and
J.P. Nunes et al. / Catena 61 (2005) 210–228216
Govers, 1988). Transport capacity is calculated from the stream power and the sediment
mean particle diameter following Govers (1990). MEFIDIS assumes that rills form over
the entire length of the cell, with widths totaling the total flow width (calculated as
described above). Finally, the particle sedimentation velocity is related with particle
diameter following Stoke’s Law (Chapra, 1997).
3.1.2. Implementation
The MEFIDIS model is implemented as a Windowsk-based program, using the
inovaGIS package for direct interaction with Geographical Information Systems
(InovaGIS, 2001). The model is forced by rainfall breakpoint data and uses a basin-
average initial soil moisture parameter. Altimetry and flow direction maps must be
supplied to the model; channel location can also be used, along with specific width and
Manning roughness values for any number of channel sections.
Table 1 shows the parameters required by MEFIDIS in a spatially distributed form;
spatial information can be given directly or supplied by appropriate surrogate maps, such
as soil maps for texture and hydraulic properties, and land-use maps for the remaining
parameters (Grayson and Bloschl, 2001). Care should be taken to represent the spatial
information at a high resolution to insure good model performance (e.g. Braun et al., 1997;
Schoorl et al., 2000); for example, Walker and Wilgoose (1999) suggest a minimum
resolution of 100�100 m for altimetry to capture local topographic details. Temporal
resolution should be related with the spatial resolution, not only to ensure model stability
but also to minimize numerical dispersion (Chapra, 1997).
MEFIDIS results include maps of interception, infiltration, surface runoff, and
accumulated soil loss, for user-selected intervals. The model also generates aggregated
information for the entire watershed, and saves time-series for user-selected points.
3.2. Model evaluation
The evaluation of MEFIDIS was performed using seven rainfall events for the
Ganspoel catchment and nine events for the Lucky Hills 103 catchment; event rainfall,
runoff and erosion characteristics are shown in Table 2. The model was applied using a
Table 1
Spatially distributed parameters required by MEFIDIS
Class Symbol Units Description
Soil texture d50 mm Mean particle diameter
Sclay – Mass fraction of clay
joc kPa Critical shear stress
Soil hydraulic properties Ksat mm/h Saturated hydraulic conductivity
h – Porosity
w mm Matric potential
Land cover Dmax mm Depression storage capacity
Imax mm Interception capacity
n – ManningTs roughness coefficientPcover – Pavement cover
Vcover – Vegetation canopy cover
Table 2
Characteristics of events used in the model evaluation exercise
Event date Rainfall
(mm)
Mean rainfall
intensity (mm/h)
Runoff
(mm)
Peak runoff
rate (mm/h)
Net soil
loss (ton/ha)
Ganspoel
19-May-1997a 10 25 0.23 0.33 0.082
21-May-1997b 3 25.7 0.16 0.18 0.025
11-Jul-1997 19.5 33.4 2.15 2.79 0.387
23-Aug-1998a,c 22.5 2.9 0.47 0.15 0.007
24-Aug-1998b,d 10 10.9 0.13 0.12 0.006
9-Sep-1998 10.5 9.8 0.31 0.22 0.013
14-Sep-1998a,b,c 41 5.3 9.19 3.3 0.595
Lucky Hills 103
12-Aug-1982a 6.6 32 0.34 2.98 0.082
23-Aug-1982 30.7 19.2 5.12 12.03 0.913
10-Sep-1982 18.8 12.6 3.38 9.02 0.721
10-Sep-1983 26.7 20.3 6.55 15.94 0.878
20-Sep-1983a 18.5 34.8 2.09 6.02 1.145
1-Sep-1984a 32.8 33 15.55 47.67 3.075
14-Jul-1985 13.7 16.3 0.38 1.87 0.101
14-Jul-1985b 10.7 20 1.18 5.68 0.374
2-Aug-1985 5.9 42 0.58 4.35 0.137
a Event used for calibration.b 100% soil water saturation assumed.c 0.1 mm baseflow not considered.d 0.2 mm baseflow not considered.
J.P. Nunes et al. / Catena 61 (2005) 210–228 217
spatial resolution of 5�5 m and a temporal resolution of 1 s. A split-sample calibration/
validation test was performed using data collected at the outlet, taking three events for
calibration and the remaining ones for validation. Calibration events were selected to
represent the largest possible range of measured conditions, as model performance usually
diminishes for events outside the calibration interval (Favis-Mortlock et al., 2001).
The objective of this exercise was to assess model performance using a single set of
calibrated parameters and general assumptions of soil moisture (Si); in this case, soil
moisture was considered at full capacity when an event equal or greater than 10 mm
occurred in the 6 h before the beginning of the simulation, and at field capacity in the
remaining cases. Test variables were total runoff, peak runoff rates, and net erosion.
Model agreement with outlet measurements does not necessarily mean that results
within the watershed are also adequately simulated (Jetten et al., 2003). To assess within-
catchment model performance for Lucky Hills 103, available runoff measurements for the
nested 101 sub-basin (Fig. 1) were evaluated in the same way as the outlet measurements.
For Ganspoel, a spatial comparison between simulated and mapped patterns of erosion and
deposition was performed for the events that occurred in May 1997. These maps indicate
the location of erosion features (rills and gullies) and deposition as observed in this period.
Although these features might reflect the consequences of all erosive storms since the
previous tillage operations, spatial patterns were considered to remain stable throughout
the period.
J.P. Nunes et al. / Catena 61 (2005) 210–228218
4. Results
4.1. Calibration procedure
The calibration storms were used to derive a best fit parameter set, used subsequently in
model validation. Initial values for the parameters described in Table 1 were taken from
measurements; rock fragment cover in Lucky Hills 103 was represented by Pcover.
Measurements were not available for Dmax, Imax and d50 in both cases; h, w and n values
were also lacking for Lucky Hills 103. Dmax was calculated from random roughness
following Kamphorst et al. (2000). Imax was calculated from Leaf Area Index values
compiled by Scurlock et al. (2001), following Hoyningen-Huene (1983). Values for d50were calculated from soil texture measurements using a fractal approach (Bittelli et al.,
1999). Soil texture was used to estimate h and w for Lucky Hills 103 following Chow et
al. (1988), while n was selected based on land cover (USDA, 1986).
Calibration focused mainly on Ksat and Dmax; a comparison between calibrated and
measured values for these parameters is shown in Table 3. It should be noted that, for both
catchments but especially for Ganspoel, calibrated Ksat values are significantly lower than
the average measurements. An explanation can be found in the fact that MEFIDIS uses the
Green–Ampt method to calculate infiltration rates; Chow et al. (1988) refer that the Ksat
parameter used in this method is a bfieldQ parameter, significantly lower than the hydraulic
Table 3
Calibrated hydraulic conductivity and depression storage capacity compared with measured values
Land use Saturated hydraulic conductivity—Ksat Depression storage capacity—Dmax
Calibrated (mm/h) Measured (mm/h) Calibrated (mm) Estimateda (mm)
Ganspoel
Beetb 38 37.6–540.3 2 2.5–3.1
(crusted)c 4.2 4.2–32.1 1.8
Forest 35 3.4–362.6 2.5 2.8
Meadow 15 2.7–151.1 2 2.8
Fallow (crusted)b 1.5 1.1–25.3 3 5.6
Maizeb 18 17.3–120 1.8 2
(crusted)c 4.5 4.2–32.1
Potatoesb 38 37.6–540.3 2.5 2.5
(crusted)c 7.5 1.1–25.3
Summer Cerealsc 8 1.9–319.9 2.4 2.2–3.4
Winter Cereals 8 1.9–319.9 2 2.5
Track – – 1.4 1.4
Road – – 1.4 1.4
Building – – 1.4 1.4
Lucky Hills 103
Shrubd 8 9.8 7.5 5.6
a Dmax values estimated following Kamphorst et al. (2000), with an error of 3 mm.b Values calibrated and validated for 1998 only.c Values calibrated and validated for 1997 only.d Dmax values estimated for California shrub.
J.P. Nunes et al. / Catena 61 (2005) 210–228 219
conductivity for saturated soil. Soil erosion was calibrated by changing d50 from 0.022
mm to 0.02 mm for Ganspoel and from 0.11 mm to 0.1 mm for Lucky Hills 103.
One difficulty in estimating a common parameter set for the Ganspoel catchment is the
significant variation in vegetation cover with season, with consequences for surface
roughness. Four Vcover and n parameter sets were estimated, one for each month when
simulated events occurred; Vcover was taken directly from measured values, and n was
estimated using a regression with random roughness and vegetation cover (Jetten, personal
communication). Another difficulty in Ganspoel is the difference in surface crusting
conditions observed during the simulated events; this impacts soil infiltration rates (Cerdan
et al., 2001) and surface storage (Darboux et al., 2001). For half of the analyzed land-cover
types, two sets of parameters were calibrated for Ksat and Dmax, but one set was validated
for 1997 only and the other for 1998 only; the effects of crusting on soil erodibility were
not taken into account. Overall, it was impossible to find a common parameter set for
every storm in Ganspoel due to the variable conditions; this would require a significant
number of additional storm events for calibration and validation.
4.2. Watershed results
Table 4 shows the model results for both watersheds, compared with measured values at
the outlet for runoff, peak runoff and net erosion; Fig. 3 compares the results for net
erosion with the 1:1 line of agreement. The correlation between the simulated and
observed results after normalization (Table 5) is quite good, showing that MEFIDIS
Table 4
Measured and simulated results for the events detailed in Table 2
Event date Runoff Peak runoff Net erosion
Measured
(mm)
Simulated
(mm)
Measured
(mm/h)
Simulated
(mm/h)
Measured
(ton/ha)
Simulated
(ton/ha)
Ganspoel
19-May-1997a 0.23 0.29 0.33 0.45 0.082 0.084
21-May-1997 0.16 0.11 0.18 0.14 0.025 0.008
11-Jul-1997 2.15 2.00 2.79 2.13 0.387 0.303
23-Aug-1998a 0.47 0.17 0.15 0.12 0.007 0.008
24-Aug-1998 0.13 0.14 0.12 0.15 0.006 0.012
09-Sep-1998a 0.31 0.47 0.22 0.79 0.013 0.162
14-Sep-1998 9.19 4.10 3.30 2.03 0.595 0.409
Lucky Hills 103
12-Aug-1982a 0.34 0.11 2.98 0.55 0.082 0.013
23-Aug-1982 5.12 6.16 12.03 9.78 0.913 1.377
10-Sep-1982 3.38 0.91 9.02 1.53 0.721 0.171
10-Sep-1983 6.55 9.62 15.94 22.01 0.878 1.941
20-Sep-1983a 2.06 3.65 6.02 8.71 1.145 0.819
01-Sep-1984a 15.55 16.17 47.67 38.05 3.075 3.377
14-Jul-1985 0.39 2.00 1.87 5.72 0.101 0.437
14-Jul-1985 1.18 3.00 5.69 7.15 0.374 0.671
02-Aug-1985 0.58 0.15 4.35 0.66 0.137 0.023
a Event used for calibration.
Fig. 3. Measured and simulated results for net erosion in Ganspoel and Lucky Hills 103, compared with the 1:1
agreement line (logarithmic scale).
J.P. Nunes et al. / Catena 61 (2005) 210–228220
performs well in predicting the relative consequences of storms. The Nash–Sutcliffe
efficiency index (Beven, 2000) is also widely used as an indicator of model performance;
the index measures the variance of the simulated results from the 1:1 prediction line, with
values above 0.5 considered to be satisfactory (Morgan and Quinton, 2001). In this case
(Table 5), this index indicates a good agreement between simulated and observed results,
with values ranging between 0.61 and 0.87.
An analysis of the average unsigned error (Table 5) shows a significant dispersion
around the 1:1 line of agreement, with values ranging from 37% to 47%; in other words,
MEFIDIS performs better in terms of accuracy than in terms of precision. However, this
error must be compared with variability in erosion measurements; Nearing et al. (1999)
found that the variability in measured soil erosion from replicated plots, under similar
rainfall, soil and surface conditions, decreased with increasing magnitude of soil loss, from
150% for a measured soil loss of 0.1 ton/ha to 14% for measured soil loss of 200 ton/ha.
Although extrapolation of plot values for watersheds is difficult, this implies that at least a
part of the model error can be explained due to variability in net erosion measurements and
Table 5
Overall correlation coefficient, Nash–Sutcliffe efficiency index and average unsigned error for the results shown
in Table 4
Runoff Peak runoff Net erosion
Ganspoel Correlation coefficienta 0.96
( p=0.01)
0.93
( p=0.01)
0.88
( p=0.01)
Nash–Sutcliffe efficiency index 0.61 0.80 0.81
Average unsigned error (%) 46 38 40
Lucky Hills 103 Correlation coefficienta 0.89
( p=0.01)
0.85
( p=0.01)
0.86
( p=0.01)
Nash–Sutcliffe efficiency index 0.87 0.85 0.7
Average unsigned error (%) 37 37 47
a Correlation between the squared roots of measured and observed values.
J.P. Nunes et al. / Catena 61 (2005) 210–228 221
surface condition factors which are difficult to estimate with precision. This conclusion is
supported by the fact that the relative difference between simulated and measured results
(calculated following Nearing et al., 1999) for Lucky Hills 103 significantly decreases
with soil loss magnitude (Fig. 4; the correlation coefficient between measured erosion and
relative difference is �0.77).
This fact also helps to explain the high values for the Nash–Sutcliffe index, when
considering that values above 0.7 are not expected due to the uncertainty inherent to field
measurements (Morgan and Quinton, 2001). Not only is there large variance between
measurements due to the selected range of events, but this index is biased towards model
performance for the larger magnitudes (Beven, 2000), where it is significantly better.
For the Ganspoel catchment, average unsigned error values do not vary significantly
with storm magnitude. One cause for this may be that the observed event magnitude in
Ganspoel is smaller than that observed for Lucky Hills 103. However, a more likely
explanation might rest with the propensity of loess soils to crusting; when crusting is not
dynamically simulated (as is the case for MEFIDIS), the model error may increase with
event magnitude (Jetten et al., 2003). When the model was calibrated individually for each
event by adjusting only Ksat and Dmax to reflect the possible crusting effects of previous
rainfall conditions and within-event storm magnitude, i.e. lowering both to represent
increased soil crusting (Cerdan et al., 2001; Darboux et al., 2001) down to the lowest
measured values (Table 3), model results improved substantially (Fig. 5). The average
unsigned error dropped to 14–15% for runoff, peak runoff and net erosion. These results
indicate that the model could be improved by a better description of the crusting effects, at
least in the case of the Ganspoel catchment.
Finally, one significant factor for the lack of model precision can be the simplified
assumptions taken for initial soil moisture, a parameter to which most runoff and erosion
models are highly sensitive (Jetten et al., 1999, 2003). The percent error margin, however,
is still small compared with the variability within measured conditions for both watersheds
(one order of magnitude for peak runoff rates and two orders of magnitude for both runoff
and net erosion; see Table 2), which shows that the model performs well for the selected
catchments and land-use conditions.
Fig. 4. Relationship between erosion magnitude and relative difference between measured and simulated values
(the error divided by the sum of measured and simulated values) for the Lucky Hills 103 catchment.
Fig. 5. Comparison of simulated and measured net erosion in Ganspoel, with MEFIDIS using a standard
calibration for all storms and a unique calibration per storm.
J.P. Nunes et al. / Catena 61 (2005) 210–228222
4.3. Within-watershed runoff rates
Simulated values for runoff and peak runoff for the Lucky Hills 101 sub-watershed
were also compared with measured values (Table 6). Lucky Hills 101 represents around
35% of the Lucky Hills 103 catchment area (Fig. 1). A comparison of model results shows
that there is a slight increase in the average unsigned error when compared with the
simulations for the entire catchment (Table 4); in relative terms, the errors are higher for
total runoff (40%) and lower for peak runoff (30%). While the smaller number of events
measured at Lucky Hills 101 might explain the differences in error, these results indicate
that MEFIDIS has a good performance in simulating runoff rates within the Lucky Hills
103 watershed.
4.4. Spatial patterns of erosion and deposition
Observed areas of rill/gully erosion and sedimentation in Ganspoel for May 1997 were
compared with the simulated results for the two events occurring in that month (Table 2).
The simulated erosion map was calculated by adding the spatially distributed model results
for erosion and deposition for both events.
Table 6
Measured and simulated results for the events detailed in Table 2, for Lucky Hills 101
Event date Runoff Peak runoff
Measured (mm) Simulated (mm) Measured (mm/h) Simulated (mm/h)
12-Aug-1982 0.18 0.06 3.20 0.23
23-Aug-1982 5.59 7.04 22.92 15.06
10-Sep-1982 2.94 0.92 10.25 2.31
20-Sep-1983 2.65 4.25 18.04 15.04
01-Sep-1984 14.70 17.83 54.85 65.58
14-Jul-1985a 0.36 2.58 – –
02-Aug-1985 0.14 0.07 1.36 0.81
J.P. Nunes et al. / Catena 61 (2005) 210–228 223
Fig. 6 compares simulated and observed erosion and deposition areas. A direct
comparison is difficult since the threshold erosion rate above which these areas are
mapped is not known; an arbitrary threshold of 5 ton/ha was selected for both erosion and
deposition to create the map showing simulated patterns. The figure shows that MEFIDIS
was capable of locating the main sediment sources and sinks within the Ganspoel
catchment during this period. The model was also able to assign major erosion features to
the appropriate fields.
These results also show that the simulated maps of erosion and deposition are not
reliable when considering a resolution of 5�5 m. One source of errors appears to be the
fact that roads were not taken into account when building the flow directions map, leading
to significant areas of erosion and deposition at roadsides. Another problem is that
Fig. 6. Simulated (top) and observed (bottom) patterns of erosion (grey) and deposition (black) in Ganspoel, for
May 1997; lines represent field boundaries.
J.P. Nunes et al. / Catena 61 (2005) 210–228224
observed erosion areas represent only 1.7% of the total catchment area, while deposition
areas represent only 0.4% of the total. Significant erosion patterns are more likely to occur
on regions of concentrated flow (Foster, 1982); errors in flow routing when considering
only eight possible directions, as is the case of MEFIDIS, can cause significant errors in
locating these areas (Costa-Cabral and Burges, 1994). This can be seen in Fig. 6, where the
simulated erosion patterns are much more dispersed than the observed patterns; the latter
either occur uniformly over slopes or along flow lines.
Similar results were obtained by Jetten et al. (2003) for the LISEM erosion model,
where flow routing determination is done in a similar way to the MEFIDIS approach
(Jetten and de Roo, 2001); in that case, simulated erosion rates with a 10�10-m resolution
were only correlated with observed values when the resolution was resampled to 50�50
m. Jetten et al. (2003) indicate that one source of this positional error might lie with flow
path delineation; another source of uncertainty referred is the high spatial variability of
parameters assumed constant by the model. The latter case appears to be a common
problem of spatially distributed models (Morgan and Quinton, 2001).
The displacement error of simulated erosion and deposition patterns was estimated by
calculating average erosion and deposition rates according to their distance to observed
features. This was done by creating a map representing this distance in 5-m increments,
and calculating the average model results for erosion and deposition inside each class;
the results are shown in Fig. 7. In both cases, simulated rates decrease sharply with
distance to the mapped areas. Beyond a distance of ca. 75 m for erosion and ca. 60 m
for deposition, both erosion and deposition rates remain constant and below a threshold
of ca. 0.5 ton/ha. When considering this threshold, MEFIDIS accuracy in classifying
regions without erosion or deposition (the largest part of the catchment) is 85.2%. In
absolute terms, 75% of the mass of eroded soil came from within 65 m of mapped soil
erosion regions, and 75% of the mass of deposited soil occurred within 105 m of
mapped deposition regions. These results show that MEFIDIS was able to reasonably
locate sediment sources and sinks inside Ganspoel for May 1997, although with a low
precision.
Fig. 7. Variation of average simulated erosion and deposition rates with distance to observed erosion and
deposition features in Ganspoel, for May 1997.
J.P. Nunes et al. / Catena 61 (2005) 210–228 225
5. Discussion and conclusions
Overall, the results of this simulation exercise show that MEFIDIS can be applied to
watersheds using common calibrated parameter sets and simplified assumptions on soil
moisture with good accuracy; model precision is less satisfactory, although it is in part
related to the uncertainty surrounding erosion measurements and improves with event
magnitude. The precision of the results is still sufficient to estimate runoff and soil erosion
rates when considering the range of events selected for the evaluation exercise. For the
Lucky Hills 103 test site, a single parameter set could be defined that provided good results
for all analyzed events, including the Lucky Hills 101 nested watershed. For Ganspoel,
however, different parameter sets were required to reflect changes in land-use, vegetation
growth and surface conditions. This indicates that in complex watersheds, model
calibration and validation must rely on measured events for several land-use scenarios;
similar results have been found for other models (e.g. Morgan and Quinton, 2001).
The performance of MEFIDIS in detecting soil erosion patterns for Ganspoel was
difficult to evaluate due to the nature of the observations, but it is clear that small-scale
precision should not be expected. The main factor is apparently the algorithm used to
delineate flow routing paths; these results are comparable to those of Jetten et al. (2003)
for LISEM. Improved performance could come from designing flow paths taking into
account roads (Duke et al., 2003) or tillage direction (Takken et al., 1999). Another
possibility is taking into account two-dimensional flow paths instead of limiting them to a
single direction (Costa-Cabral and Burges, 1994; Liu et al., 2004); however, this would
require a significant shift in the conceptualization of MEFIDIS, and possibly a revision of
the one-dimensional flow equations (Chow et al., 1988).
One way to improve model precision for Ganspoel appears to be a better estimation of
surface crusting conditions and their reflection on surface properties. Simple assumptions
per land-cover type and condition can be established using data from remote sensing (e.g.
Baghdadi et al., 2002; Oh, 2004) or laboratory studies (e.g. Assouline and Mualem, 2000);
an example of this approach can be found in Cerdan et al. (2001).
Overall, the results show that MEFIDIS can be a robust tool for predicting the effects of
change in storm characteristics for runoff, peak runoff rates and soil erosion, for the same
watershed and land-use conditions. The model also performed well in predicting the
general location of significant erosion features, indicating its usefulness as a spatially
distributed risk assessment tool. However, the potential to simulate changes in land-use
patterns and vegetation properties requires further analysis with more extensive datasets
both for calibration and validation. The capacity to simulate within-catchment erosion and
deposition rates also requires further evaluation.
Acknowledgements
This work was funded by the National Board for Scientific and Technological Research
(JNICT) and the General-Directorate for the Environment (DGA) under contract no.
PEAM/C/84/91. Joao Nunes acknowledges the support given by the Foundation for
Science and Technology (FCT) and the European Union under Operational Program
J.P. Nunes et al. / Catena 61 (2005) 210–228226
bScience, Technology, and InnovationQ (POCTI), PhD grant ref. SFRH/BD/5059/2001,
inserted in the IIIrd Community Support Framework (2000–2006). The authors also wish
to thank the Laboratory of Experimental Geomorphology at Leuven (Belgium) and the
USDA-ARS Southwest Watershed Research Center at Tombstone (Arizona, USA) for
providing the data used in this study. Finally, the authors wish to thank two anonymous
reviewers for their valuable contributions to this manuscript.
References
Assouline, S., Mualem, Y., 2000. Modeling the dynamics of soil seal formation: analysis of the effect of soil and
rainfall properties. Water Resour. Res. 36 (8), 2341–2349.
Baghdadi, N., King, C., Bourguignon, A., Remond, A., 2002. Potential of ERS and Radarsat data for surface
roughness monitoring over bare agricultural fields: application to catchments in Northern France. Int. J.
Remote Sens. 23 (17), 3427–3442.
Beven, K., 2000. Rainfall–Runoff Modelling—the Primer. John Wiley & Sons, Chichester.
Bittelli, M., Campbell, G.S., Flury, M., 1999. Characterization of particle-size distribution in soils with a
fragmentation model. Soil Sci. Soc. Am. J. 63 (4), 782–788.
Braun, P., Molnar, T., Kleeberg, H.-B., 1997. The problem of scaling in grid-related hydrological process
modelling. Hydrol. Process. 11, 1219–1230.
Cerdan, O., Souchere, V., Lecomte, V., Couturier, A., Le Bissonais, Y., 2001. Incorporating soil surface crusting
processes in an expert-based runoff model: sealing and transfer by runoff and erosion related to agricultural
management. Catena 46, 189–205.
Chapra, S.C., 1997. Surface Water-Quality Modeling. McGraw-Hill, New York.
Chow, V.T., Maidment, D.R., Mays, L.W., 1988. Applied Hydrology. McGraw-Hill, New York.
Costa-Cabral, M.C., Burges, S.J., 1994. Digital elevation model networks (DEMON): a model of flow over
hillslopes for computation of contributing and dispersal areas. Water Resour. Res. 30 (6), 1681–1692.
Darboux, F., Davy, P., Gascuel-Odoux, C., Huang, C., 2001. Evolution of soil surface roughness and flowpath
connectivity in overland flow experiments. Catena 46, 125–139.
de Roo, A.P.J., Wesseling, C.G., Ritsema, C.J., 1996a. LISEM: a single event physically-based hydrological and
soil erosion model for drainage basins: I—theory, input and output. Hydrol. Process. 10 (8), 1107–1117.
de Roo, A.P.J., Offermans, R.J.E., Cremers, N.H.T.D., 1996b. LISEM: a single event physically-based
hydrological and soil erosion model for drainage basins: II—sensitivity analysis, validation and application.
Hydrol. Process. 10 (8), 1119–1126.
Duke, G.D., Kienzle, S.W., Johnson, D.L., Byrne, J.M., 2003. Improving overland flow routing by incorporating
ancillary road data into Digital Elevation Models. J. Spat. Hydro. 3 (2), 1–27.
Favis-Mortlock, D., Boardman, J., MacMillan, V., 2001. The limits of erosion modeling: why we should proceed
with care. In: Harmon, R.S., Doe, W.W. (Eds.), Landscape Erosion and Evolution Modeling. Kluwer
Academic/Plenum Publishers, New York, pp. 477–516.
Ferreira, A.G., Singer, M.J., 1985. Energy dissipation for water drop impact into shallow pools. Soil Sci. Soc.
Am. J. 49 (6), 1537–1542.
Flanagan, D.C., Nearing, M.A., 1995. USDA Water Erosion Prediction Project: hillslope profile and watershed
model documentation. NSERL Report no. 10, USDA-ARS National Soil Erosion Research Laboratory, West
Lafayette.
Foster, G.R., 1982. Modeling the erosion process. In: Haan, C.T., Johnson, H.P., Brakensiek, D.L. (Eds.),
Hydrologic Modeling of Small Watersheds. American Society of Agricultural Engineers, St. Joseph,
pp. 295–380.
Govers, G., 1990. Empirical relationships for the transporting capacity of overland flow. Int. Assoc. Hydrol. Sci.
Publ. 189, 45–63.
Grayson, R., Bloschl, G., 2001. Summary of pattern comparison and concluding remarks. In: Grayson, R.,
Bloschl, G. (Eds.), Spatial Patterns in Catchment Hydrology—Observations and Modelling. Cambridge
University Press, Cambridge, pp. 355–367.
J.P. Nunes et al. / Catena 61 (2005) 210–228 227
Hoyningen-Huene, J.V., 1983. Die Interzeption des Niederschlages in landwirtschaftlichen Pflanzenbestanden.
Verlag Paul Parey, Hamburg, Berlin.
Huggins, L.F., Burney, J.R., 1982. Surface runoff, storage, and routing. In: Haan, C.T., Johnson, H.P., Brakensiek,
D.L. (Eds.), Hydrologic Modeling of Small Watersheds. American Society of Agricultural Engineers,
St. Joseph, pp. 167–226.
inovaGIS, 2001. Geographical Information Interoperable Technology. Published online at http://www.
inovagis.org.
Jetten, V.G., de Roo, A.P.J., 2001. Spatial analysis of erosion conservation measures with LISEM. In: Harmon,
R.S., Doe, W.W. (Eds.), Landscape Erosion and Evolution Modeling. Kluwer Academic/Plenum Publishers,
New York, pp. 429–445.
Jetten, V., de Roo, A., Favis-Mortlock, D., 1999. Evaluation of field-scale and catchment-scale soil erosion
models. Catena 37 (4), 521–541.
Jetten, V., Govers, G., Hessel, R., 2003. Erosion models: quality of spatial predictions. Hydrol. Process. 17,
887–900.
Kamphorst, E.C., Jetten, V., Guerif, J., Pitkanen, J., Iversen, B.V., Douglas, J.T., Paz, A., 2000. Predicting
depressional storage from soil surface roughness. Soil Sci. Soc. Am. J. 64 (5), 1749–1758.
Linsley, R.K., Kohler, M.A., Paulhus, J.L.H., 1975. Hydrology for Engineers, 2nd ed. McGraw-Hill, New York.
Liu, Q.Q., Chen, L., Li, J.C., Singh, V.P., 2004. Two-dimensional kinematic wave model of overland flow. J.
Hydrol. 291, 28–41.
McCarthy, J., Canziani, O., Leary, N., Dokken, D., White, K., 2002. Climate Change 2001: Impacts, Adaptation,
and Vulnerability. Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge.
Milly, P.C.D., Wetherald, R.T., Dune, K.A., Delworth, T.L., 2002. Increasing risk of great floods in a changing
climate. Nature 415, 514–617.
Morgan, R.P.C., Quinton, J.N., 2001. Erosion modeling. In: Harmon, R.S., Doe, W.W. (Eds.), Landscape Erosion
and Evolution Modeling. Kluwer Academic/Plenum Publishers, New York, pp. 117–143.
Morgan, R.P.C., Quinton, J.N., Smith, R.E., Govers, G., Poesen, J.W.A., Chisci, G., Torri, D., 1998. The
EUROSEM model. In: Boardman, J., Favis-Mortlock, D.T. (Eds.), Modeling Soil Erosion by Water, NATO-
ASI Series I-55. Springer, Berlin, pp. 389–398.
Nachtergaele, J., Poesen, J., Vandekerckhove, L., Wijdenes, D.O., Roxo, M., 2001. Testing the ephemeral gully
erosion model (EGEM) for two Mediterranean environments. Earth Surf. Process. Landf. 26 (1), 17–30.
Nearing, M.A., Govers, G., Norton, L.D., 1999. Variability in soil erosion data from replicated plots. Soil Sci.
Soc. Am. J. 63, 1829–1835.
Oh, Y., 2004. Quantitative retrieval of soil moisture content and surface roughness from multipolarized radar
observations of bare soil surfaces. IEEE Trans. Geosci. Remote Sens. 42 (3), 596–601.
Rauws, G., Govers, G., 1988. Hydraulic and soil mechanical aspects of rill generation on agricultural soils. J. Soil
Sci. 39, 111–124.
Schoorl, J.M., Sonneveld, M.P.W., Veldkamp, A., 2000. Three-dimensional landscape process modelling: the
effect of DEM resolution. Earth Surf. Process. Landf. 25, 1025–1034.
Scurlock, J.M.O., Asner, G.P., Gower, S.T., 2001. Worldwide Historical Estimates and Bibliography of Leaf
Area Index, 1932–2000. ORNL Technical Memorandum TM-2001/268. Oak Ridge National Laboratory,
Oak Ridge.
Senior, C.A., Jones, R.G., Lowe, J.A., Durman, C.F., Hudson, D., 2002. Predictions of extreme precipitation
and sea-level rise under climate change. Philos. Trans. R. Soc. Lond. Ser. A: Math. Phys. Sci. 360 (1796),
1301–1311.
Sharma, P.P., Gupta, S.C., Rawls, W.J., 1991. Soil detachment by single raindrops of varying kinetic-energy. Soil
Sci. Soc. Am. J. 55 (2), 301–307.
Sharma, P.P., Gupta, S.C., Foster, G.R., 1993. Predicting soil detachment by raindrops. Soil Sci. Soc. Am. J. 57
(3), 674–680.
Smith, R.E., Goodrich, D.C., Woolhiser, D.A., Unkrich, C.L., 1995. KINEROS—a kinematic runoff and erosion
model. In: Singh, V.J. (Ed.), Computer Models of Watershed Hydrology, Water Resources Publications,
pp. 697–732.
SWCS—Soil and Water Conservation Society, 2003. Conservation Implications of Climate Change: Soil Erosion
and Runoff from Cropland. Soil and Water Conservation Society, Ankeny.
J.P. Nunes et al. / Catena 61 (2005) 210–228228
Takken, I., Beuselinck, L., Nachtergaele, J., Govers, G., Poesen, J., Degraer, G., 1999. Spatial evaluation of a
physically-based distributed erosion model (LISEM). Catena 37, 431–447.
Toy, T.J., Foster, G.R., Renard, K.G., 2002. Soil Erosion: Processes, Prediction, Measurement, and Control. John
Wiley & Sons, Inc., New York.
USDA—United States Department of Agriculture, 1986. Urban hydrology for small watersheds, Natural
Resources Conservation Service, Conservation Engineering Division, Technical Release 55.
Walker, J.P., Wilgoose, G.R., 1999. On the effect of digital elevation model accuracy on hydrology and
geomorphology. Water Resour. Res. 35 (7), 2259–2268.
Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion losses, a guide to conservation planning.
Agriculture Handbook, vol. 282. United States Department of Agriculture.
Wu, T.H., Hall, J.A., Bonta, J.V., 1993. Evaluation of runoff and erosion models. ASCE J. Irrig. Drain. Eng. 119
(4), 364–381.